When calculating a confidence interval for the difference between two means, what information are you gaining?

The means are from both same population and different?

Thank you.

You are gaining information about the population. You are estimating the difference in population means by using the difference in the sample means. You also make a few assumptions, such as the populations have the same variance and the populations are normally distributed.

When calculating a confidence interval for the difference between two means, you are gaining information about the range within which the true difference between the population means is likely to fall.

To calculate a confidence interval, you need the following information:

1. Sample means: You need the sample mean of the first group (mean1) and the sample mean of the second group (mean2).

2. Sample sizes: You need the number of observations in the first group (n1) and the number of observations in the second group (n2).

3. Standard deviations or standard errors: Depending on the information available, you can either use the standard deviations of the two groups (s1 and s2) or the standard errors (SE1 and SE2). The standard error is the standard deviation divided by the square root of the sample size.

If the means are from the same population, you are essentially comparing two different samples from the same population. In this case, you would need to calculate the pooled standard deviation (sp) based on the individual standard deviations (s1 and s2) using the formula:

sp = sqrt([(n1 - 1) * s1^2 + (n2 - 1) * s2^2] / [n1 + n2 - 2])

If the means are from different populations, you would consider them as two independent groups, and you would not need to calculate the pooled standard deviation. Instead, you would directly use the standard errors (SE1 and SE2) obtained using the sample sizes and standard deviations of each group.

Once you have the necessary information, you can calculate the confidence interval using a statistical formula. The confidence interval provides a range of values within which you can be confident (at a specified level, e.g., 95%) that the true difference between the population means lies.

Remember, calculating a confidence interval helps you estimate the range within which the true difference between the means is likely to fall, based on sample data. It is important to interpret the interval properly, considering the level of confidence and the specific context of the data analysis.